What is the projection of #< -3, 7, 7># onto #< -3 , 4, -5>#?

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Answer 1 · 2017-10-19T12:04:10

The projection is #=1/25<-3,4,-5>#

The vectors are

#veca=<-3,7,7>#

#vecb=<-3,4,-5>#

The projection of #veca# onto #vecb# is

#proj_(vecb)veca=(veca.vecb)/(||vecb||^2)vecb#

#=(<-3,7,7>.<-3,4,-5>)/(||<-3,4,-5>||^2)<-3,4,-5>#

#=((-3)^2+(7.4)+(7.-5))/((-3)^2+(4.4)+(-5.-5))<-3,4,-5>#

#=(2/50)<-3,4,-5>#

#=1/25<-3,4,-5>#